# 11) A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

Let l and bare the length and breadth of rectangle respectively and r will be  the radius of circle
The total perimeter of window = perimeter of rectangle + perimeter of the semicircle

=

Area of window id given by (A) =

Now,

Hence, b = 5/2 is the point of maxima

Hence, these are the  dimensions of the window to admit maximum light through the whole opening

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